The field of the invention is systems and methods for magnetic resonance imaging (“MRI”). More particularly, the invention relates to systems and methods for correcting motion-induced phase errors in diffusion-weighted MRI.
Diffusion-weighted MRI is a powerful tool to evaluate the microstructure of tissues based on the diffusion of water molecules within those tissues. Because diffusion encoding is essentially the encoding of motion, any type of motion will be reflected in the received signal or, equivalently, the reconstructed image. It has been previously shown by A. W. Anderson and J. C. Gore, in “Analysis and Correction of Motion Artifacts in Diffusion Weighted Imaging,” Magn Reson Med, 1994; 32:379-387, that coherent motion of an imaging object during the diffusion-encoding period results in phase errors in the reconstructed image. These motion-induced phase errors can be ignored in single-shot diffusion imaging when only a magnitude image is used, as is often the case in practice. However, single-shot imaging can only be used if the required resolution is relatively low, or if reduced field-of-view imaging is used so that a single-shot acquisition can be realized without much distortion. When high resolution is needed, however, such as for three-dimensional full brain diffusion-weighted imaging (“DWI”), the data acquisition readout window for a single-shot acquisition is so long that T*2 blurring or significant image distortion from magnetic field inhomogeneities are introduced into the resultant images. In these cases, a multi-shot acquisition is usually implemented. When multi-shot acquisitions are used, the k-space data are divided into multiple partitions, or shots, each of which is acquired in different excitations and acquisition windows. Therefore, different shots of the image acquisition carry different motion-induced phase errors. The differing phase errors, if not corrected, can result in significant artifacts in the final reconstruction. As a result, multi-shot acquisitions are always used in combination with some type of motion-induced phase error correction.
While many algorithms exist for the correction of motion-induced phase errors in two-dimensional DWI, motion-induced phase error correction in three-dimensional DWI is still under development. The difficulties associated with three-dimensional motion-induced phase error correction include the acquisition of a true three-dimensional navigator and the development of algorithms for phase error estimation and correction in three-dimensions. Realization of a true three-dimensional navigator with high enough resolution to capture the nonlinearity of the motion-induced phase errors is nontrivial, especially for pulse sequences that require short repetition times (“TR”), such as diffusion-weighted steady-state imaging. Regarding phase error estimation and correction, several studies have tried to extend the existing two-dimensional motion-induced phase error correction methods. For example, J. Zhang, et al., in “3D Self-Navigated Interleaved Spiral (3D-SNAILS) for DWI,” 15th Annual Meeting of ISMRM, Berlin, Germany, 2007; p. 9, described extending the two-dimensional self-navigated interleaved spiral (“SNAILS”) to three dimensions, and L. R. Frank, et al., in “High Efficiency, Low Distortion 3D Diffusion Tensor Imaging with Variable Density Spiral Fast Spin Echoes (3D DW VDS RARE),” Neuroimage, 2010; 49:1510-1523, described extending a simultaneous phase correction and SENSE reconstruction approach to three-dimensions. However, these extensions of existing two-dimensional techniques to three dimensions included limitations that restricted their practical use. In the case of the SNAILS technique, the performance of the resulting algorithm was trajectory dependent, thereby limiting its practical use for three-dimensional acquisitions, and in many cases, the image reconstruction time was too long for practical use.
If the only source of motion-induced phase errors is rigid body motion, the resulting phase errors in the reconstructed image are linear, which means that the phase errors are equivalent to shifts and constant phase-offsets in k-space. Utilizing this idea, a time-efficient motion-induced phase error correction method was recently introduced by Y. Jung, et al., in “3D Diffusion Tensor MRI with Isotropic Resolution Using a Steady-State Radial Acquisition,” J Magn Reson Imaging, 2009; 29:1175-1184. In this method, the magnitude peaks of the navigator k-space data were used to estimate k-space shifts and phase offsets induced by motion-induced phase errors. The corrupted data were then corrected in k-space correspondingly. However, because the navigator data was only a one-dimensional radial line through the center of k-space, the phase error estimation and correction was only one-dimensional. Furthermore, the performance of this method depended on the resolution of the navigators in k-space. Results from Y. Jung, et al., show significant residual phase errors after correction that had to be further taken into account by discarding data.
Another algorithm for correcting motion-induced phase errors induced by rigid body motion referred to as the three-dimensional k-space and image space correction technique (“3D KICT”) was described recently by A. T. Van, et al., in “K-Space and Image Space Combination for Motion-Induced Phase Error Correction in 3D Diffusion-Weighted Imaging,” 17th Annual Meeting of ISMRM, Honolulu, Hi., 2009; p. 1381. In this method, k-space shifts are estimated as by unwrapping and fitting linear phase errors to one-dimensional linear functions in image space separately along the x-, y-, and z-directions. The phase of the peak k-space navigator data point is then used for the constant phase offset estimation. The correction is then performed in k-space, resulting in k-space trajectories and data that are corrected for shot-dependent phase errors. Unlike the previously discussed algorithm proposed by Jung, et al., only the performance of the constant phase offset estimation is dependent on the resolution in k-space of the navigator. The k-space shift estimation is independent of the k-space resolution of the navigator, as it is performed as a slope estimation in image space. However, this linear fitting estimation method is highly sensitive to noise, especially in the case of small phase errors.
It would therefore be desirable to provide a method for correcting motion-induced phase errors in three-dimensions, and in which the method provides clinically practical image reconstruction times and is generally insensitive to noise.